Preheat the oven to 350˚F.
Beat the butter, cream cheese and sugar in the bowl of an electric mixer, until light and fluffy, about 4-5 minutes.
Add the eggs, one at a time, and beat for 1 minute before adding the next one.
Gradually add the dry ingredients: flour, baking powder and baking soda, and beat until well incorporated, 3-4 minutes.
Add half of the lemon juice and beat until well mixed.
In a small bowl, toss the blueberries with flour.
With a spatula, fold the lemon zest and the blueberries into the batter.
Pour the batter into de bundt pan and make it even with a spatula.
Over a kitchen towel in the counter, firmly tap pan to level batter an release air.
Bake for 55 minutes or until a toothpick inserted in center of cake comes out clean.
Let cool down for 10 minutes.
In a small bowl, mix the resting 3 lemon juice tablespoons with the confectioners' sugar.
Unmold the cake and while still warm, poke it with a bamboo skewer.
Pour the syrup on top and let cool down completely before serving it.